Normal generators of finite fields
نویسندگان
چکیده
منابع مشابه
Generators and irreducible polynomials over finite fields
Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of Hansen-Mullen.
متن کاملPeriod Distribution of Inversive Pseudorandom Number Generators Over Finite Fields
In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field (ZN ,+,×), where N > 3 is a prime. The sequences generated by the IPRNGs are transformed to 2-dimensional linear feedback shift register (LFSR) sequences. By employing the generating function method and the finite field theory, the period distribution is obtain...
متن کاملGenerators of Nonassociative Simple Moufang Loops over Finite Prime Fields
The first class of nonassociative simple Moufang loops was discovered by L. Paige in 1956 [9], who investigated Zorn’s and Albert’s construction of simple alternative rings. M. Liebeck proved in 1987 [7] that there are no other finite nonassociative simple Moufang loops. We can briefly describe the class as follows: For every finite field F, there is exactly one simple Moufang loop. Recall Zorn...
متن کاملGenerators of Finite Fields with Powers of Trace Zero and Cyclotomic Function Fields
Using the relation between the problem of counting irreducible polynomials over finite fields with some prescribed coefficients to the problem of counting rational points on curves over finite fields whose function fields are subfields of cyclotomic function fields, we count the number of generators of finite fields with powers of trace zero up to some point, answering a question of Z. Reichste...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1992
ISSN: 0022-314X
DOI: 10.1016/0022-314x(92)90114-5